Transformation Plots
Plotting the original category values against their corresponding quantifications can reveal trends that might not be noticed in a list of the quantifications. Such plots are commonly referred to as transformation plots. Attention should be given to categories that receive similar quantifications. These categories affect the predicted response in the same manner. However, the transformation type dictates the basic appearance of the plot.
Variables treated as numerical result in a linear relationship between the quantifications and the original categories, corresponding to a straight line in the transformation plot. The order and the difference between the original categories is preserved in the quantifications.
The order of the quantifications for variables treated as ordinal correspond to the order of the original categories. However, the differences between the categories are not preserved. As a result, the transformation plot is nondecreasing but need not be a straight line. If consecutive categories correspond to similar quantifications, the category distinction may be unnecessary and the categories could be combined. Such categories result in a plateau on the transformation plot. However, this pattern can also result from imposing an ordinal structure on a variable that should be treated as nominal. If a subsequent nominal treatment of the variable reveals the same pattern, combining categories is warranted. Moreover, if the quantifications for a variable treated as ordinal fall along a straight line, a numerical transformation may be more appropriate.
For variables treated as nominal, the order of the categories along the horizontal axis corresponds to the order of the codes used to represent the categories. Interpretations of category order or of the distance between the categories is unfounded. The plot can assume any nonlinear or linear form. If an increasing trend is present, an ordinal treatment should be attempted. If the nominal transformation plot displays a linear trend, a numerical transformation may be more appropriate.
The following figure displays the transformation plot for Price, which was treated as numerical. Notice that the order of the categories along the straight line correspond to the order of the original categories. Also, the difference between the quantifications for $1.19 and $1.39 (–1.173 and 0) is the same as the difference between the quantifications for $1.39 and $1.59 (0 and 1.173). The fact that categories 1 and 3 are the same distance from category 2 is preserved in the quantifications.
The nominal transformation of Package design yields the following transformation plot. Notice the distinct nonlinear shape in which the second category has the largest quantification. In terms of the regression, the second category decreases predicted preference ranking, whereas the first and third categories have the opposite effect.